A building is 30 meters high and is on top of a hill. The angles of
elevation of the top and bottom of the building from a point at the foot
of the hill are 64 degrees and 58 degrees respectively. How high is the
hill?

A network engineer seeks help integrating a trigonometric expression with a cosine
term in its denominator (or is it the cotangent?). Using double-angle identities and a
substitution, Doctor Ali provides a boost.

Finding the inverse of a function and graphing yields a graph that has
been reflected in the line y = x relative to the function. Inverse
proportionality, however, yields a reciprocal relation graphically.
Why do these two things have similar names yet mean different things?